

from collections.abc import Callable

import numpy as np





def 	__a     (      A__			:  str			,  A__			:  Any			,  A__			:  Optional[int]			,  A__			:  List[Any]			,  A__			:  Tuple       ):
    SCREAMING_SNAKE_CASE										=   int(np.ceil((x_end - xa) / step_size       )       )
    SCREAMING_SNAKE_CASE										=   np.zeros((n + 1,)       )
    SCREAMING_SNAKE_CASE										=   ya
    SCREAMING_SNAKE_CASE										=   xa

    for k in range(A_       ):
        SCREAMING_SNAKE_CASE										=   y[k] + step_size * ode_func(A_			,  y[k]       )
        SCREAMING_SNAKE_CASE										=   y[k] + (
            (step_size / 2) * (ode_func(A_			,  y[k]       ) + ode_func(x + step_size			,  A_       ))
        )
        x += step_size

    return y


if __name__ == "__main__":
    import doctest

    doctest.testmod()

import math

def a__       (			A_   ):






  '''simple docstring'''





  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5,	int(math.sqrt(A_   ) + 1   ),	6   ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True

def a__       (			A_ = 0.1   ):






  '''simple docstring'''





  __magic_name__								=			3
  __magic_name__								=			3

  while primes / (2 * j - 1) >= ratio:
    for i in range(j * j + j + 1,	(j + 2) * (j + 2),	j + 1   ):
      primes += is_prime(A_   )
    j += 2
  return j


if __name__ == "__main__":
    import doctest

    doctest.testmod()

